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Consider two matrices:

a = [1 2 3; 4 5 6; 7 8 10]

a =

1 2 3

4 5 6

7 8 10

and b=a + 10

b =

11 12 13

14 15 16

17 18 20

first, I am trying to obtain all possible combination of rows (1st row of 'a' and all rows of 'b', second row of 'a' and all rows of 'b' and so on) such that the output is

c =

1 2 3 11 12 13

4 5 6 11 12 13

7 8 10 11 12 13

1 2 3 14 15 16

4 5 6 14 15 16

7 8 10 14 15 16

1 2 3 17 18 20

4 5 6 17 18 20

7 8 10 17 18 20

secondly for each row, I am storing the first 3 and the last 3 columns in a single index of a 3 index vector. So in this example the vector of combosets is 2x3x9 where element is

combosets(:,:,1) =

1 2 3

11 12 13

combosets(:,:,2) =

4 5 6

11 12 13

and so on. The code I am using is below. Is there any better and faster way to do this and prefarably step 1 and 2 combined?

Thanks in advance!

clc

clearvars;

a = [1 2 3; 4 5 6; 7 8 10]; % 3 by 3 matrix

b=a + 10; % 3 by 3 matrix

r=size(a,1);

combosets=zeros(r-1,r,r*r);

d={NaN};

% Step 1: storing different combination of rows in cell

for k=1:1:r

c=vertcat(horzcat(a(:,:),repmat(b(k,:),r,1)),horzcat(a(:,:),repmat(b(k,:),r,1)),horzcat(a(:,:),repmat(b(k,:),r,1)));

d{k}=(unique(c,'rows'));

end

ddash=cell2mat(d'); % making it a matrix again

% Step 2: storing in a multidimensional array

for j=1:1:r*r

rowset1=ddash(j,1:3);

rowset2=ddash(j,4:6);

combosets(:,:,j)=[rowset1;rowset2];

end

Johannes Fischer
on 8 Sep 2020

a = [1 2 3; 4 5 6; 7 8 10]; % 3 by 3 matrix

b=a + 10; % 3 by 3 matrix

r=size(a, 1);

% create repetitions of values

a = repmat(a, [r, 1]);

b = repelem(b, r, 1);

% create combination matrix

c = [a b];

% reshape into combosets

combosets = reshape(c', 3, 2, 9);

% permute to get dimensions right

combosets = permute(combosets, [2, 1, 3]);

Adam Danz
on 8 Sep 2020

Edited: Adam Danz
on 8 Sep 2020

Fast & clean 2-liner:

a = [1 2 3; 4 5 6; 7 8 10];

b = a + 10;

c = [repmat(a,size(b,1),1), repelem(b, size(a,1),1)];

combosets = permute(reshape(c.',3,2,9),[2,1,3]);

Adam Danz
on 8 Sep 2020

"I wish I could accept more than 1 answer"

You accepted the right one if it works for your data and it make sense to you. The time difference is so small that readability and understandability are important factors. Plus, I like when newer contributors get recognition for their contributions and encouragement to continue doing so ðŸ™‚.

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